# About the BPSK signal waveform

My basic knowledge is too bad. I am confused about the waveform of BPSK signals. To create a BPSK signal, I generated BPSK symbols with ideal rectangle pulse shaping, which is given by: Then, the signal after carrier modulation is shown below, which is consistent with the waveform on the textbook. But, the root raise cosine (RRC) filter is often used in practical. By using the same BPSK symbols above, the waveform after pulse shaping is given by:

After carrier modulation, the waveform becomes like this: This strange image makes me wonder, is this the correct waveform? Because there is no such waveform in the textbook，I am really not sure about that, Thanks guys. By the way, I have tried that this modulated signal can be demodulated after coherent demodulation and matched filter.

Modulated symbols after pulse-shaping: After carrier modulation: • If you are able to demodulate the signal, it should be the correct one. Oct 9 '18 at 9:05
• It does not look right to me as the resulting waveform should just be your pulse shape multiplied by your carrier, but perhaps this is an artifact of the short symbols. Can you also generate a very long sequence of ones followed by a very long sequence of zeros using your same approach? Oct 10 '18 at 2:17
• Sure, you can see the following figures. Are they look right? Oct 17 '18 at 8:55

If you can demodulate then it's probably correct. Perhaps it's just the fact that the carrier is not very fast that it looks weird. Can you increase the symbol period and the carrier frequency. Otherwise, my guess is that you are not convolving correctly. Just double-check if your RC has the correct width (or zero crossings). For reference I generated this:

Pulse-shaped BPSK with rect() through convolution: Modulated by multiplying with the carrier tone: Now with the raised-cosine pulse shape: Note that by sampling at the correct times (each symbol period), we can recover the BPSK sequence perfectly.